[PPT] - MODELING AND ANAL YSIS OF TRAFFIC IN HIGH SPEED NETW ORKS PowerPoint Presentation

SLIDE 1 MODELING AND ANAL YSIS OF TRAFFIC IN HIGH SPEED NETW ORKS A CTS A TM In ternet w

rk

Pro ject Information and T elecomm unication T ec hnology Cen ter Univ ersit y

f

Kansas.

SLIDE 2 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Organization

Motiv

ation F ailure

f

Classical Mo dels.

In

tro duction. Long Range Dep endence.

Analytical

Mo del. Macro-dynamics Micro-dynamics

P

erformance Analysis Metho dology . Mean Cell dela y . Cell loss probabilit y .

Data

collection pro cess and the AAI Net w

rk.

A CTS A TM In ternet w

rk

Pro ject 1

SLIDE 3 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Organization (con td.)

Sim

ulation Mo del. Mo del Description. V alidation.

Exp

erimen tal Ev aluation. Mean Cell dela y and Cell Loss Probabilit y results. T rac Micro-dynamics. Sensitivit y

f

n um b er

f

phases. Second-order statistics.

Conclusions.
F

uture W

rk.

A CTS A TM In ternet w

rk

Pro ject 2

SLIDE 4 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Motiv ation

T

rac studies.

Queueing

p erformance

f

a pro cess with innite v ariance.

Switc

h buers get lled up faster than those predicted b y con v en tional mo dels

Example:

Mean cell dela y:

(A) 1 Load Mean Delay (B)

Figure 1: T ypical Dela y curv es for long-range dep enden t mo del (B) and con v en tional mo del (A). A CTS A TM In ternet w

rk

Pro ject 3

SLIDE 5 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Motiv ation (con td.)

Example:

Probabilit y

f

Cell Loss:

P(Q>x) Buffer Size log( , x (B) (A) )

Figure 2: T ypical loss curv es for long-range dep enden t mo del (B) and con v en tional mo del (A).

T

rac mo deling and p erformance prediction required for ecien t

p

erational algorithms. A CTS A TM In ternet w

rk

Pro ject 4

SLIDE 6 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

In tro duction

Self

similar trac mo dels: FBM, ARIMA, Mo deling with Chaotic Maps.

Denition
f

self similarit y: Let X = (X t , t= 0, 1, 2...) b e a co v ariance stationary pro cess X k (m) = 1 m m1 X i=0 X k mi (1) Exactly: r (m) (k ) = r (k ); k

(2)

Asymptotically: r (m) (k ) ! r (k ); m ! 1 (3) A CTS A TM In ternet w

rk

Pro ject 5

SLIDE 7 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

In tro duction (con td.)

Ramications

Non-summable auto correlation function. Div ergen t P

w

er-Sp ectrum at the

rigin.
Implication

Burstiness

f

Aggregate trac.

Origin

ON-OFF source frame-w

rk

with ON and OFF p erio ds that follo w a distribution with innite v ariance. A CTS A TM In ternet w

rk

Pro ject 6

SLIDE 8 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

T rac Mo del

Denition:

Rate Pro cess: A random pro cess R (t), whic h is the short-term time a v erage

f

the arriv al pro cess A(t).

5 10 15 0.5 1 1.5 2 2.5 x 10

9

Time (Hours) Number of Cells 5 10 15 5 10 15 20 25 30 35 40 45 Time(Hours) Rate(Mb/s)

Cell coun t pro cess Rate pro cess. A CTS A TM In ternet w

rk

Pro ject 7

SLIDE 9 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

T rac Mo del (con td.)

Mo

del the Macro-dynamics and Micro-dynamics

f

the Rate Pro cess.

Rate

pro cess is mo deled as a non-Mark

vian

, stationary and ergo dic phase-pro cess ha ving a nite state space S=fx 1 ; x 2 ; :::x N g.

k Time Rate x x x N 1 x 1

A CTS A TM In ternet w

rk

Pro ject 8

SLIDE 10 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

T rac Mo del (con td.)

The

rate v ector

=

[ 1 ;

2

; :::;

N

+1 ] represen ts the b

undary

rates for the states and

1
1
::::
N

+1 .

Time Rate γ . N+1 γ N γ 1 2 γ γ k . .

A CTS A TM In ternet w

rk

Pro ject 9

SLIDE 11 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

T rac Mo del (con td.)

The

probabilit y v ector

=

[ 1 ;

2

; :::;

N

] denotes the steady-state probabilit y v ector

f

the phase pro cess.

The

steady state phase probabilities

f

the phase pro cess are assumed to follo w a distribution with a hea vy tail.

The

rates in

and

the probabilit y v ector

dene

the macro-dynamics. A CTS A TM In ternet w

rk

Pro ject 10

SLIDE 12 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

T rac Mo del (con td.)

is
btained

b y partitioning the range [ min , max ] where

min

and

max

represen t the minim um and maxim um rates resp ectiv ely .

The

rate v ector

for

N phases is:

1

=

min

(4)

i

=

1

+

max
min

N ; i = 2; 3; 4; :::; N (5)

N

+1 =

max

: (6) A CTS A TM In ternet w

rk

Pro ject 11

SLIDE 13 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

T rac Mo del (con td.)

is
btained

from the CDF

f

R (t).

The

CDF

f

R (t) can b e

btained

from a theoretical innite v ariance distribution. Here, a theoretical P areto Distribution w as used. A P areto Distribution can b e giv en as: F X (x) = 1

K

x

;
>

1; x > K : (7) The maxim um lik eliho

d

estimate

f

the shap e parameter

,

for a giv en set

f

data samples D = fd 1 ; d 2 ; ::; d M g is giv en as

=

1 1 M P M i=1 l n(d i ) (8) A CTS A TM In ternet w

rk

Pro ject 12

SLIDE 14 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

T rac Mo del (con td.)

The

CDF can also b e

btained

from an empirical CDF

f

the rate pro cess.

The

steady-state probabilit y

i

for state x i , whic h is b

unded

b y rates

i

and

i+1

is computed as:

i

= P [X

i+1

]

P

[X

i

]; i = 1; 2; 3:::N

1

= F X ( i+1 )

F

X ( i ); i = 1; 2; 3:::; N

1

(9)

1 RATE γ γ γ γ γ 2 3 4 Ν+1 1 γ Ν CDF

Figure 3: Quan tizing the CDF

f

R (t). A CTS A TM In ternet w

rk

Pro ject 13

SLIDE 15 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

T rac Mo del (con td.)

Within

eac h state x i , with asso ciated probabilit y

i

, the arriv al pro cess is mo deled as a p

in

t pro cess with a with nite mean

i+1

and nite v ariance.

The

distribution function denes the trac micro-dynamics

f

that state.

Assuming
i+1

as the mean rate in state x i is a conserv ativ e assumption as it is the upp er b

und
n

the rates in eac h state. A CTS A TM In ternet w

rk

Pro ject 14

SLIDE 16 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

P erformance Analysis Metho dology

Let

Z denote the random v ariable asso ciated with a p erformance parameter

f

a queue with R (t) as the input pro cess.

x 2 x

R

3 x 1 x 4 x n x i

Figure 4: Concept for p erformance analysis metho dology .

F
llo

wing the linearit y prop ert y

f

exp ected v alue, the exp ected v alue

f

the random v ariable Z can b e written as E [Z ] = X i2S

i

E [Z jS = x i ] (10)

In

the ab

v

e equation the trac macro-dynamics are describ ed b y the v alues

f
and

the micro-dynamics are represen ted b y E [Z jS = x i ]. A CTS A TM In ternet w

rk

Pro ject 15

SLIDE 17 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

P erformance Analysis Metho dology (con td.)

P

erformance prediction in terms

f

Mean Cell Dela y and Cell loss Probabilit y .

Notation:

Let Slotted system, innite buer. n denote the n um b er

f

cells in the system at a giv en time. P i n (j ) represen ts the probabilit y that there are n cells in the queue at the end

f

the j th slot, giv en that the input pro cess is in state x i . p i k denote the probabilit y that there are k arriv als to the system when the input pro cess is in state x i .

Queue

dynamics are describ ed b y: P i n (j + 1) = n+1 X k =0 P i k (j )p i n(k 1) + (11)

(x)

+ represen ts the maxim um

f

f0; xg. A CTS A TM In ternet w

rk

Pro ject 16

SLIDE 18 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

P erformance Analysis Metho dology (con td.)

Mean-Dela

y: Slotted-G/ D/ 1 system, analysis based

n

Probabilit y Generating F unction (PGF). Av erage cell dela y giv en as: E [D ] = 1

N

X i=1

i

1

i

f 1 2

2

i + 3 2

2

i g (12) where = P N i=1

i
i+1

is the mean arriv al rate. D is the random v ariable represen ting the dela y exp erienced b y cells arriving at the input

f

the queueing system.

i

, is the probabilit y that the system is

ccupied

i.e., the utilization giv en S = x i A CTS A TM In ternet w

rk

Pro ject 17

SLIDE 19 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

P erformance Analysis Metho dology (con td.)

Cell

loss Probabilit y Let P L [K jS = x i ] denote cell loss probabilit y in a nite buer

f

size K , giv en that the input pro cess is in state x i .

P

L [K jS = x i ] is appro ximated as P [Q > K jS = x i ] P L [K jS = x i ]

P

[Q > K ] (13)

Analysis
f

Cell loss for a General arriv al pro cess to a slotted system is hard. Assume that the micro-dynamics are exp

nen

tial. P L (K ) = N X i=1

i

(1

K

X k =0 (1

i

)p i k + P i n=1 f1

P

n m=0 p i m gP i k n p i ) (14) p i n = e

i
i

n n! (15) A CTS A TM In ternet w

rk

Pro ject 18

SLIDE 20 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Summary

f

Metho dology

Obtain

( min ;

max

).

Obtain

the CDF

f

the rate pro cess. The CDF can b e

btained

as a { theoretical distribution, for example using

,

the shap e parameter

f

a P areto distribution. {

r

can b e calculated from a giv en collected data trace.

Quan

tize the CDF in to 'N' lev els, where lev el i is represen ted b y rate

i+1

in the v ector

.
The

probabilit y

f

b eing in the state x i is giv en b y the elemen t

i

in the v ector

as
i

= F( i+1 )-F( i ).

Giv

en the linearit y prop ert y

f

exp ected v alue E [Z ] = P i2S

i

E [Z jS = x i ] A CTS A TM In ternet w

rk

Pro ject 19

SLIDE 21 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Data Collection Pro cess and the AAI.

P

erformance Analysis is based

n

T race data collected from the AAI net w

rk.
Conguration:

aai-pop.nrl.aai.net aai-pop-ether.nccosc.aai.net aai-pop-ether.nrlssc.aai.net aai-pop-ether.cewes.aai.net

AAI

CEWES NRL ARL NRLSSC NCCOSC GSD

aai-pop-ether.gsd.aai.net aai-pop-ether.arl.aai.net

SWITCH SITE

KU

merlin.edc.magic.net

EDC TIOC

hettz.tioc.magic.net spork.tisl.ukans.edu OC 3 OC 3 OC 3 OC 3 OC 3 OC 3 OC 3 OC 3 OC 12

Figure 5: Connections

f

the sites and switc hes b eing sampled. A CTS A TM In ternet w

rk

Pro ject 20

SLIDE 22 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Data Collection Pro cess and the AAI(con td.)

Data

collected from sev eral edge switc hes using Simple Net w

rk

Managemen t Proto col (SNMP).

T
tal

Data collected:

1.8

Gb ytes.

Sampling

in terv al is appro ximately 60 seconds.

Data

w as re-sampled using linear in terp

lation

so that sampling in terv al is exactly 60 seconds.

120 60 Cell conts Time

t t2 1 c(t 2) c(t 1) c(k t k ∆ t) ∆

Figure 6: Re-sampling b y linear in terp

lation
f

cell coun ts. A CTS A TM In ternet w

rk

Pro ject 21

SLIDE 23 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Data Collection Pro cess and the AAI (con td.)

Re-sampling:

c(k t) = c(t 1 ) + c(t 2 )

c(t

1 ) t 2

t

1

(k

t

t

1 ); k = 1; 2; 3; ::: (16) where c(k t) is the cell coun t

btained

b y in terp

lation.

t is the time in terv al after re-sampling and is 60 seconds. c(t 2 ) and c(t 1 ) are cell coun ts from collected data whic h are sampled at appro ximately 60 seconds.

The

rate pro cess R (t) can no w b e

btained

as: R (t) = c(t + 60)

c(t)

60 (17) A CTS A TM In ternet w

rk

Pro ject 22

SLIDE 24 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Sim ulation Mo del

Queueing

Mo del is an innite buer with a deterministic serv er.

Time

is slotted with a single cell serv ed at the end

f

the slot.

Sim

ulation based

n

calculating the "unnished w

rk"

in the queue at the end

f

a slot, from the equation: n(k + 1) = max(0; n(k ) + a(k )

1):

(18) where n(k ) is the n um b er

f

cells in the system at the end

f

the k th slot. a(k ) is the n um b er

f

cells that arriv ed during the k th slot. max(a; b) represen ts the maxim um

f

the quan tities a and b. A CTS A TM In ternet w

rk

Pro ject 23

SLIDE 25 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Sim ulation Mo del (con td.)

n(k-1) TIME Number of Cells k k+1 k-1 n(k) n(k+1)

Figure 7: Dela y estimation from cell coun ts

Mean

Cell dela y is giv en b y:

=

1 M M X k =1 n(k )

(19)

A CTS A TM In ternet w

rk

Pro ject 24

SLIDE 26 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Sim ulation Mo del (con td.)

In

Equation (19)

is

mean cell dela y

v

er the whole trace and M is the total n um b er

f

slots for the giv en trace.

is

the rate

f

the deterministic rate

f

the serv er in cells/sec.

Probabilit

y

f

Cell loss: The cell loss probabilit y for a buer size x denoted as P L (x), is

btained

b y coun ting the relativ e n um b er

f

times, the queue length n(k ) exceeds the v alue x. P L (x) = P [n(k ) > x] (20) A CTS A TM In ternet w

rk

Pro ject 25

SLIDE 27 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Sim ulation Mo del (con td.)

V

alidation: Sim ulator v alidated for Mean Dela y and Cell loss. { By comparing sim ulation results with those predicted b y standard theoretical results. { Source whic h generates cells with exp

nen

tially distributed in ter-arriv al times with a kno wn a v erage rate has b een constructed. { Exp

nen

tial in ter-arriv als generated using T ransform Metho d. A CTS A TM In ternet w

rk

Pro ject 26

SLIDE 28 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Sim ulation Mo del (con td.)

Sampled cell counts

SOURCE

Figure 8: V alidation

f

Mo del

Output
f

the source sampled at constan t time in terv als

f

T S seconds

Sim

ulates the data collection pro cess.

T

S =60 seconds as in the case

f

collected data.

Queueing

system is a M/ D/ 1 system for whic h theoretical results are a v ailable.

Considering

the statistical nature

f

the sim ulation, sim ulation results closely agree with the exp erimen tal results. A CTS A TM In ternet w

rk

Pro ject 27

SLIDE 29 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 27

SLIDE 30 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 4 6 8 10 12 14 16 18 20 x 10

−3

Load Mean Cell Delay Simulation Theory

Figure 9: V alidation

f

the sim ulator for mean cell transfer dela y results. A CTS A TM In ternet w

rk

Pro ject 28

SLIDE 31 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 28

SLIDE 32 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

10 20 30 40 50 60 70 80 −9 −8 −7 −6 −5 −4 −3 −2 −1 Buffer Size Log(P(X>x) Simulation Theory

Figure 10: V alidation

f

the sim ulator for Cell loss ratio results. A CTS A TM In ternet w

rk

Pro ject 29

SLIDE 33 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Exp erimen tal Ev aluation

Exp

erimen tal Ev aluation done b y comparing the p erformance predicted b y the mo del, with the sim ulation results

btained

from the AAI net w

rk.
T

races used: T able 1: Data traces used for mo del v alidation T race Name Duration (Hours) # cells Characteristic Mean Rate(Mb/s) NCCOSC 25 3.02697e08 Bac kground 1.55795 Phillips 15 2.227e09 SC '95 20.3064 NRL 6 5.1054e08 EMMI 10.307321

T

races c hosen suc h that dieren t trac lev els are used.

T

race T yp es: { Bac kground: Managemen t Flo ws, routing up dates etc. { EMMI: Multimedia trac proles. { SC '95

ws:

Burst y application trac proles t ypical in wide area A TM net w

rks.

A CTS A TM In ternet w

rk

Pro ject 30

SLIDE 34 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 30

SLIDE 35 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

5 10 15 20 25 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Time(Hours) Rate(Mb/s)

Figure 11: Data Collected from NCCOSC site. A CTS A TM In ternet w

rk

Pro ject 31

SLIDE 36 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 31

SLIDE 37 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 Load Mean Cell Delay (Seconds) Simulation Histogram Pareto/Exponential model

Figure 12: Mean Cell Dela y estimate

btained

from theory ( = 8:2), histogram and sim ulation for the trace lab eled 'NCCOSC' and sho wn in Figure 11, using N = 15 input phases. A CTS A TM In ternet w

rk

Pro ject 32

SLIDE 38 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 32

SLIDE 39 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

10 20 30 40 50 60 −9 −8 −7 −6 −5 −4 −3 −2 −1 Buffer Size, x Log10(P(Q>x)) Simulation Histogram Pareto/Exponential model

Figure 13: Comparison

f

cell loss probabilit y estimates

btained

from theory ( = 8:2), histogram and sim ulation

f

the collected data trace lab eled NCCOSC and sho wn in Figure 11, using N = 15 input phases.

=

:4. A CTS A TM In ternet w

rk

Pro ject 33

SLIDE 40 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 33

SLIDE 41 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

5 10 15 5 10 15 20 25 30 35 40 45 Time(Hours) Rate(Mb/s)

Figure 14: Data trace Collected from the Phillips site. A CTS A TM In ternet w

rk

Pro ject 34

SLIDE 42 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 34

SLIDE 43 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.05 0.1 0.15 0.2 0.25 Load Mean Cell Delay (Seconds) Simulation Histogram Pareto/Exponential model

Figure 15: Comparison

f

Mean Cell Dela y estimates

btained

from theory ( = 1:2), histogram and sim ulation

f

the collected data trace lab eled Phillips and sho wn in Figure 14, using N = 15 input phases. A CTS A TM In ternet w

rk

Pro ject 35

SLIDE 44 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 35

SLIDE 45 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

20 40 60 80 100 120 −9 −8 −7 −6 −5 −4 −3 −2 −1 Buffer Size, x Log10(P(Q>x)) Simulation Histogram Pareto/Exponential model

Figure 16: Comparison

f

cell loss probabilit y estimates

btained

from theory ( = 1:2), histogram and sim ulation

f

the collected data trace lab eled Phillips and sho wn in Figure 14, using N = 15 input phases.

=

:4. A CTS A TM In ternet w

rk

Pro ject 36

SLIDE 46 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 36

SLIDE 47 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

1 2 3 4 5 6 5 10 15 20 25 Time (Hours) Rate(Mb/s)

Figure 17: Data trace Collected from the NRL site. A CTS A TM In ternet w

rk

Pro ject 37

SLIDE 48 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 37

SLIDE 49 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Load Mean Cell Delay (Seconds) Simulation Histogram Pareto/Exponential model

Figure 18: Comparison

f

Mean Cell Dela y estimates

btained

from theory ( = 2:2), histogram and sim ulation

f

the collected data trace lab eled NRL and sho wn in Figure17, using N = 15 input phases. A CTS A TM In ternet w

rk

Pro ject 38

SLIDE 50 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 38

SLIDE 51 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

10 20 30 40 50 60 70 −8 −7 −6 −5 −4 −3 −2 −1 Buffer Size, x Log10(P(Q>x)) Simulation Histogram Pareto/Exponential model

Figure 19: Comparison

f

cell loss probabilit y estimates

btained

from theory ( = 2:2), histogram and sim ulation

f

the collected data trace lab eled NRL and sho wn in Figure 17 using N = 15 input phases.

=

:4. A CTS A TM In ternet w

rk

Pro ject 39

SLIDE 52 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 39

SLIDE 53 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Theory

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 4 6 8 10 12 14 16 18 20 x 10

−4

Mean Cell Delay (Sec) Load Exponential Uniform

Figure 20: Eect

f

trac micro-dynamics

n

Mean Dela y predicted b y theory ( = 8:2) for the trace lab eled 'NCCOSC' and sho wn in Figure 11, using N = 15 input phases. A CTS A TM In ternet w

rk

Pro ject 40

SLIDE 54 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 40

SLIDE 55 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Sim ulation

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 4 6 8 10 12 14 16 18 20 x 10

−4

Load Mean Cell Delay (Sec) Exponential Uniform

Figure 21: Eect

f

trac micro-dynamics

n

Mean Dela y

btained

from sim ulation

f

the trace lab eled 'NCCOSC' and sho wn Figure 11. A CTS A TM In ternet w

rk

Pro ject 41

SLIDE 56 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 41

SLIDE 57 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

5 10 15 20 25 30 35 40 45 50 −9 −8 −7 −6 −5 −4 −3 −2 −1 Buffer size, x Log10(P(Q>x)) load=.4 load=.7 Exponential Uniform

Figure 22: Eect

f

trac micro-dynamics

n

Cell loss probabilit y

btained

from sim ulation

f

the trace lab eled 'NCCOSC' and sho wn Figure 11. A CTS A TM In ternet w

rk

Pro ject 42

SLIDE 58 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 42

SLIDE 59 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

0.3 0.4 0.5 0.6 0.7 0.8 −7 −6 −5 −4 −3 −2 −1 Load Log10(P(Q>x)) Exponential Uniform

Figure 23: Eect

f

trac micro-dynamics

n

Cell loss probabilit y estimate

btained

for a xed buer size

f

15 cells from sim ulation

f
n

the trace lab eled 'NCCOSC' and sho wn in Figure 11. A CTS A TM In ternet w

rk

Pro ject 43

SLIDE 60 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 43

SLIDE 61 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Theory

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 10

−4

Load Mean Cell Delay (Secs) Exponeetial Uniform

Figure 24: Eect

f

trac micro-dynamics

n

Mean Dela y predicted b y theory ( = 1:2), for the trace lab eled 'Phillips' and sho wn in Figure 14, using N = 15 input phases. A CTS A TM In ternet w

rk

Pro ject 44

SLIDE 62 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 44

SLIDE 63 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Sim ulation

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 10

−4

Load Mean Cell Delay(Sec) Uniform Exponential

Figure 25: Eect

f

trac micro-dynamics

n

Mean Dela y

btained

from sim ulation

f

the trace lab eled 'Phillips' and Figure 14. A CTS A TM In ternet w

rk

Pro ject 45

SLIDE 64 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 45

SLIDE 65 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 −5 −4.5 −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 Load Log(P(Q>x)) Exponential Uniform

Figure 26: Eect

f

trac micro-dynamics

n

Cell loss probabilit y estimate

btained

for a xed buer size

f

30 cells from sim ulation

f

the trace lab eled 'Phillips' and sho wn Figure 14. A CTS A TM In ternet w

rk

Pro ject 46

SLIDE 66 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 46

SLIDE 67 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Theory

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 1 1.5 2 2.5 x 10

−4

Load Mean Cell Delay ( Secs) Exponential Uniform

Figure 27: Eect

f

trac micro-dynamics

n

Mean Dela y predicted b y theory ( = 2:2) for the trace lab eled NRL and sho wn in Figure 17, using N = 15 input phases. A CTS A TM In ternet w

rk

Pro ject 47

SLIDE 68 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 47

SLIDE 69 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Sim ulation

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 2 x 10

−4

Load Mean Cell Delay (Sec) Exponential Uniform

Figure 28: Eect

f

trac micro-dynamics

n

Mean Dela y

btained

from sim ulation

f

the trace lab eled NRL and sho wn in Figure 17. A CTS A TM In ternet w

rk

Pro ject 48

SLIDE 70 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 48

SLIDE 71 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

0.2 0.3 0.4 0.5 0.6 0.7 0.8 −6 −5 −4 −3 −2 −1 Load log(P(Q>x)) Exponential Uniform

Figure 29: Eect

f

trac micro-dynamics

n

Cell loss probabilit y estimate

btained

for a buer size

f

25 cells from sim ulation

f

the trace lab eled NRL and sho wn in Figure 17. A CTS A TM In ternet w

rk

Pro ject 49

SLIDE 72 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 49

SLIDE 73 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

100 200 300 400 500 600 700 800 900 1000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lag(1 unit = 60 secs) Autocorrelation Function Pareto/Exponential Trace data

Figure 30: Second

rder

statistics

btained

from trace data and P areto/Exp

nen

tial mo del for the trace lab eled 'NCCOSC' and sho wn in Figure 11. A CTS A TM In ternet w

rk

Pro ject 50

SLIDE 74 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 50

SLIDE 75 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

20 40 60 80 100 120 140 160 180 200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lag (1 unit = 60 seconds) Autocorrelation Function Pareto/Exponential Trace data

Figure 31: Second

rder

statistics

btained

from trace data and P areto/Exp

nen

tial mo del for the trace lab eled 'Phillips' and sho wn in Figure 14. A CTS A TM In ternet w

rk

Pro ject 51

SLIDE 76 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 51

SLIDE 77 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

50 100 150 200 250 300 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lag (1 unit = 60 secs) Autocorrelation Function Pareto/Exponential Trace data

Figure 32: Second

rder

statistics

btained

from trace data and P areto/Exp

nen

tial mo del for the trace lab eled 'NRL' and sho wn in Figure 17. A CTS A TM In ternet w

rk

Pro ject 52

SLIDE 78 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 52

SLIDE 79 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 Load Mean Cell Delay (Seconds) N=10 N=15 N=25 N=35

Figure 33: Eect

f

dieren t n um b er

f

phases

n

mean cell dela y demonstrated using the trace lab eled 'NCCOSC' and sho wn in Figure 11. A CTS A TM In ternet w

rk

Pro ject 53

SLIDE 80 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

A CTS A TM In ternet w

rk

Pro ject 53

SLIDE 81 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

10 20 30 40 50 60 70 80 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 Buffer Size, x Log10(P(Q>x)) N=10 N=15 N=25 N=35

Figure 34: Eect

f

dieren t n um b er

f

phases

n

cell loss probabilit y demonstrated using the trace lab eled 'NCCOSC' and sho wn in Figure 11. A CTS A TM In ternet w

rk

Pro ject 54

SLIDE 82 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

Conclusions

A

simple phase mo dulated mo del as w ell as a p erformance ev aluation tec hnique w ere dev elop ed in this study to mo del trac in wide area A TM net w

rks.
Metho

dology w as v alidated with extensiv e trace driv en sim ulations p erformed using collected data traces from the AAI A TM W AN.

The

exp erimen tal ev aluation

f

the mo del is done in terms

f

mean cell dela y and cell loss probabilit y .

The

study establishes non-P

isson

nature

f

trac

n

an early national scale A TM net w

rk,

the AAI net w

rk.
Eect
f

trac micro-dynamics

n

queueing p erformance w ere in v estigated.

In

the presence

f

LRD, mean dela y estimate is relativ ely in v arian t to the actual micro-dynamics.

A

lo w loads cell loss probabilit y w as found to b e sensitiv e to micro-dynamics.

A

t higher loads, bursts

n

the macro-scale, dominate the cell loss in the queue and the micro dynamics pla y a minor role. A CTS A TM In ternet w

rk

Pro ject 55

SLIDE 83 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks
Logarithm
f

the cell loss probabilit y has a linear relationship to load in the case

f

exp

nen

tially distributed in ter-arriv al times, but is non-linear in the case

f

real net w

rk

trace data.

Second
rder

statistics are mo deled reasonably . A CTS A TM In ternet w

rk

Pro ject 56

SLIDE 84 Mo deling and Analysis

f

T rac in High Sp eed Net w

rks

F uture W

rk
Simple

mo del

Signican

t complexit y can b e added. Eects

f

the UPC sc heme and UPC parameters.

Adding

a p erio dic comp

nen

t to tak e in to accoun t the p erio dicit y

f

the input pro cess.

Considering

the eects

f

dieren t theoretical innite-v ariance distributions.

Dev

eloping analytical expressions for studying eects

f

micro-dynamics

n

cell-loss.

Dev

eloping expressions for computing the auto correlation function n umerically .

Constructing

trac mo dels with phase dep enden t micro-dynamic distributions. A CTS A TM In ternet w

rk

Pro ject 57